This paper considers constructions of optimal designs for heteroscedastic polynomial measurement error models. Corresponding approximate design theory is developed by using corrected score function approach, which leads to non-concave optimisation problems. For the weighted polynomial measurement error model of degree p with some commonly used heteroscedastic structures, the upper bounds for the number of support points of locally D-optimal designs can be determined explicitly. A numerical example is given to show how heteroscedastic structures affect the optimal designs.

中文翻译：

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异方差多项式测量误差模型的局部 D 最优设计

本文考虑了异方差多项式测量误差模型的优化设计的构造。相应的近似设计理论是利用修正得分函数的方法发展起来的，这导致了非凹优化问题。对于具有一些常用异方差结构的 p 次加权多项式测量误差模型，可以明确确定局部 D 最优设计的支持点数的上限。给出了一个数值例子来说明异方差结构如何影响优化设计。